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How Math Unraveled the 'Hard Day's Night' Mystery

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The Beatles
It took Dalhousie University professor Jason Brown six months and some advanced mathematical analytical techniques to crack the code behind one of the most mysterious sounds in music: the “prraaaaaangg" sound at the beginning of the Beatles' “Hard Day's Night."

Guitarists have puzzled over how this chord is played for decades because it contains a note that would be impossible for the Beatles' two guitarists and bassist to play in one take, and experts have concluded that no multitracking was involved in this part of the song. The secret sauce, as it turns out, includes five piano notes apparently played by producer George Martin. Brown made the discovery by disassembling the sampled amplitudes into the original frequencies using Fourier transforms.

“What about the other three D3s? Only one can come from George's twelve-string, and even if John played another one on his six-string, there's still another to account for," reads part of the conclusion of Brown's report. “Beatles' record producer George Martin is known to have doubled on piano George Harrison's solo on the track. Could 'the chord' be part piano?"

“Pianos have three strings for every note; a hammer strikes all three at the same time to produce a sound. That solved the problem of the three F3s; all could have come from a piano playing F3."

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